Exam 4: B: probability and Probability Distributions

Driver Education Narrative Three randomly chosen 14-year-old middle school students who had not yet taken driver's education classes were given the written part of the Manitoba Driver's Exam. Each student was graded as passing (P) or failing (F) the written exam. -Maria selected two M&M candies at random from a bowl containing three M&Ms. One was red; one was yellow; and the remaining one was orange. Describe the sample space if the sampling is done with replacement.

Smoking Habits of Health Club Members Narrative A group of 40 people at a health club were classified according to their gender and smoking habits, as shown in the table below. One person is selected at random from that group of 40 people. Smoking Habits -Refer to Smoking Habits of Health Club Members Narrative. What is the probability the person is female?

Defective Bolts Narrative Approximately 5% of the bolts coming off a production line have serious defects. Two bolts are randomly selected for inspection. -In the "Quick Draw" casino card game, a player chooses one card from a deck of 52 well-shuffled cards. If the card the player selects is the king of hearts, the player wins $104; if the card is an ace, the player wins $78; if the card selected is anything else, the player loses $13. Considering a negative amount won to be a loss, how much should the player expect to win in one play of "Quick Draw"?

An Italian restaurant in Québec City offers a special summer menu in which, for a fixed dinner cost, you can choose from one of two salads, one of three entrees, and one of four desserts. How many different dinners are available?

Late Night Talk Shows Narrative Let A be the event that a randomly selected person watches the Tonight Show with Jay Leno (event A) and B be the event that a randomly selected person watches the Late Show with David Letterman (event B). It is possible to time-shift a program to a more convenient hour and thus watch both programs. Suppose the following probabilities are given: P(A B) = 0.20, P(A ) = 0.40, P( ) = 0.10, and P( ) = 0.30. -Refer to Late Night Talk Shows Narrative. Are the events A and B independent? Justify your answer.

SALES NARRATIVE A salesperson either makes a sale (S) or does not make a sale (N) with each of two potential customers. The simple events and their probabilities are given below. -Refer to Sales Narrative. What is the probability that exactly one sale is made?

Late Night Talk Shows Narrative Let A be the event that a randomly selected person watches the Tonight Show with Jay Leno (event A) and B be the event that a randomly selected person watches the Late Show with David Letterman (event B). It is possible to time-shift a program to a more convenient hour and thus watch both programs. Suppose the following probabilities are given: P(A B) = 0.20, P(A ) = 0.40, P( ) = 0.10, and P( ) = 0.30. -Refer to Late Night Talk Shows Narrative. What is the probability that a randomly selected person watches only Jay Leno?

Mall Shopper Narrative One hundred shoppers at a local shopping mall were categorized by age and gender as shown in the frequency distribution below. One shopper is selected at random from that group of 100 shoppers. Age Group -Refer to Mall Shopper Narrative. Convert the frequency table shown above into a probability table.

Psychological Tests Narrative A psychologist tests Grade 7 students on basic word association skills and number pattern recognition skills. Let W be the event a student does well on the word association test. Let N be the event a student does well on the number pattern recognition test. A student is selected at random, and the following probabilities are given: P(W N) = 0.25, P(W ) = 0.15, P( N) = 0.10, and P( ) = 0.50. -Refer to Psychological Tests Narrative. What is the probability that the randomly selected student does well on the number pattern recognition test?

Dell Computer Owners Narrative Dell computer owners are very faithful. Despite reporting s with their current systems, 90% of Dell owners said they would buy another computer from the company, based on the service they received. Suppose you randomly select three current Dell computer users and ask them whether they would buy another Dell computer system. -Refer to Dell Computer Owners Narrative. What are the population mean, variance, and standard deviation for the random variable x?

Coffee Brands Narrative A food company plans to conduct an experiment to compare its brand of coffee with that of two competitors. A single person is hired to taste each of three brands of coffee, which are unmarked except for identifying symbols, A, B, and C. -Refer to Coffee Brands Narrative. Define the experiment.

Job Applicants Narrative Five applicants apply for two jobs. Applicants A and B are male; applicants C, D, and E are female. The personnel officer selects two applicants at random to fill the two jobs. -Refer to Job Applicants Narrative. List all possible combinations of the five applicants for the two different jobs.

Political Opinions Narrative A political scientist asked a group of people how they felt about two political policy statements. Each person was to respond either A (agree), N (neutral), or D (disagree) to each policy statement. -Refer to Political Opinions Narrative. Describe the sample space; that is, list all possible response combinations to the two statements.

Salary of Working Mothers Narrative A researcher studied the relationship between the salary of a working woman with school-aged children and the number of children she had. The results are shown in the following probability table: Number of Children Let A denote the event that a working woman has two or fewer children, and let B denote the event that a working woman has a low salary. -Refer to Salary of Working Mothers Narrative. What is the probability that a working woman has two or fewer children?

Salary of Working Mothers Narrative A researcher studied the relationship between the salary of a working woman with school-aged children and the number of children she had. The results are shown in the following probability table: Number of Children Let A denote the event that a working woman has two or fewer children, and let B denote the event that a working woman has a low salary. -Refer to Salary of Working Mothers Narrative. What is the probability that a working woman has two or fewer children and has a low salary?

A professor has received a grant to travel to an archaeological dig site. The grant includes funds for three graduate students to accompany the professor. If there are six graduate students available to the professor and all the funds are to be used (i.e., three students will go), how many choices does the professor have?

Drug Offenders Narrative Research studies suggest that the likelihood a drug offender will be convicted of a drug offence within two years after treatment for drug abuse may depend on the person's educational level. The proportions of the total number of cases that fall into four education/conviction categories are shown in the table below: Status within Two Years after Treatment Suppose a single offender is selected from the treatment program. Here are two events of interest: A: The offender has 10 or more years of education. B: The offender is convicted within two years after completion of treatment. -Refer to Drug Offenders Narrative. Find P( ).

Psychological Tests Narrative A psychologist tests Grade 7 students on basic word association skills and number pattern recognition skills. Let W be the event a student does well on the word association test. Let N be the event a student does well on the number pattern recognition test. A student is selected at random, and the following probabilities are given: P(W N) = 0.25, P(W ) = 0.15, P( N) = 0.10, and P( ) = 0.50. -Refer to Psychological Tests Narrative. Are the events W and N mutually exclusive? Justify your ANS.

Fast-Food Restaurants Narrative Lily frequents one of two fast-food restaurants, choosing McDonald's 25% of the time and Burger King 75% of the time. Regardless of where she goes, she buys french fries on 60% of her visits. -Refer to Fast-Food Restaurants Narrative. The next time Lily goes into a fast-food restaurant, what is the probability that she goes to McDonald's and orders french fries?

Number of Cars Narrative Let the random variable x represent the number of cars owned by a family. Assume that x can take on five values: 0, 1, 2, 3, 4. A partial probability distribution is shown below: -Refer to Number of Cars Narrative. Find the probability that a family owns no more than one car.